Circle

Circle

A circle is a basic geometric shape that is useful throughout mathematics. It is defined a shape where every point along its perimeter is an equal distance from its center.

Property Image Description
Radius Circle Radius The radius is the distance from the center of the circle to any point along the perimeter of the circle.
Circumference Circle Circumference The circumference, denoted with the variable , is the length around the perimeter of the circle.
Diameter Circle Diameter The diameter is the distance between any two points along the perimeter of the circle that passes through the center of the circle.
Area Circle Area The area of a circle is the amount of two-dimensional space that fits inside the perimeter of the circle.

Formulas

Area of Circle | Formula

The area of a circle is give by one-half multiplied by τ (tau) mutliplied by the radius of the circle squared.

Circumference of Circle | Formula

The circumference of a circle is given the constant τ (tau) multpilied by the radius of the circle, where τ = 2π.

Equations

Equation of Circle | Concept

The standard form of a circle is given by the radius and center point of the circle.

General Equation of Circle | Concept

The standard form of the equation of a circle is given in terms of its radius and center point.

Concepts

Radians | Concept

Radians are a unit that measure angle using the radius of a circle. One radian is equal to the amount of rotation required to travel the length of one radius along the circumference of the circle.

Degrees | Concept

Degrees is a unit of measure for angles. A full rotation is equal to 360 degrees. In the cartesian coordinate system, degrees are measured starting from the rightmost edge of the circle.

Unit Circle | Concept

The unit circle is a unifying idea in mathematics that connects many useful concepts together. This article goes over the basic properties of the circle using interactive examples and explains how they connect to the trigonometric functions and pythagorean theorem.